INTRODUCTION

During human walking, a substantial amount of mechanical work is performed
on the center of mass during the step-to-step transition
(Kuo et al., 2005). Donelan et
al. used force platforms under each limb (i.e. individual limbs method) to
demonstrate that during double support, the leading leg performs negative work
to redirect the center of mass while the trailing leg performs positive work
to restore lost energy (Donelan et al.,
2002a; Donelan et al.,
2002b). The trailing leg impulse begins just prior to the leading
leg heel-strike (i.e. a pre-emptive push-off occurs), reducing the leading leg
collision and the magnitude of positive work required to redirect the center
of mass velocity (Donelan et al.,
2002a; Kuo, 2002;
Ruina et al., 2005).

Although a pre-emptive push-off can help reduce collision losses, the
trailing leg still must perform positive mechanical work during double
support. Trailing limb positive mechanical work constitutes ∼60–70%
of the total positive work performed over a stride and the ankle plantar
flexors provide the majority of that work
(Kuo et al., 2005).
Theoretical analyses of simple bipedal walking models
(Kuo, 2002;
Ruina et al., 2005) and
empirical measurements on humans (Donelan
et al., 2002a; Donelan et al.,
2002b) both indicate that step-to-step transition positive
mechanical work increases with step length to the fourth power. Net metabolic
power during human walking also increases in proportion to the fourth power of
step length (Donelan et al.,
2002a). These data indicate that the step-to-step transition
probably accounts for ∼60–70% of the total net metabolic power (W
kg–1) during walking
(Donelan et al., 2002a;
Kuo et al., 2005).

In a previous study, we showed that bilateral robotic lower-limb
exoskeletons can be used to examine the metabolic cost of ankle
muscle–tendon mechanical work during human walking
(Sawicki and Ferris, 2008). We
assumed that exoskeleton artificial pneumatic muscles directly replaced
plantar flexor muscle–tendon positive mechanical work. Reported values
of the `muscular efficiency' (η+muscle) of positive
work for mammalian skeletal muscle range from 0.10–0.34, with many
sources assuming an average of ∼0.25
(Gaesser and Brooks, 1975;
Margaria, 1968;
Ryschon et al., 1997;
Smith et al., 2005;
Whipp and Wasserman, 1969).
Comparison of changes in net metabolic power and average mechanical power at
the ankle joint in our previous exoskeleton study yielded an `apparent
efficiency' of ankle muscle–tendon positive mechanical work of 0.61 for
walking at 1.25 m s–1. Our results were indicative of the
Achilles' tendon performing ∼59% of the plantar flexor muscle–tendon
positive work (assuming η+muscle=0.25)
(Sawicki and Ferris, 2008). We
estimated that the plantar flexor muscle–tendons performed ∼35% of
the total lower limb positive mechanical work, but consumed only ∼19% of
the total metabolic energy during level walking at 1.25 m
s–1.

The purpose of the present study was to extend our previous exoskeleton
results to examine the metabolic cost of plantar flexor muscle–tendon
work at longer step lengths. Humans normally increase walking speed by
increasing both step length and step frequency. However, step-to-step
transition mechanical and metabolic energy expenditure depends most strongly
on step length (∼step length4)
(Donelan et al., 2002a;
Donelan et al., 2002b). We
chose to have our subjects increase walking speed by increasing step length
only (i.e. while holding step frequency constant). This kept
frequency-dependent metabolic costs (e.g. leg swing) constant and resulted in
larger increases in step-to-step transition mechanical and metabolic power
requirements than would be expected for natural increases in speed (see
Materials and methods for more details). We hypothesized that the `apparent
efficiency' of plantar flexor muscle–tendon positive work would decrease
at longer step lengths. We based this hypothesis on the expectation that as
speed and step length increased, the plantar flexor muscle fibers would
deliver a larger fraction of the ankle muscle–tendon positive work than
elastic energy from the recoiling Achilles' tendon. An inherent assumption of
this study was that the exoskeleton mechanical work would replace ankle
muscle–tendon mechanical work rather than augment it. As such, we
expected triceps surae muscle activation to be less during walking with the
powered exoskeletons compared to walking without exoskeleton assistance for
all speed–step length conditions. To test these predictions, we compared
subjects' net metabolic power and electromyography amplitudes with ankle
exoskeletons powered versus unpowered during level, steady-speed
walking at various step lengths and a constant step frequency (i.e. preferred
at 1.25 m s–1).

MATERIALS AND METHODS

Subjects

We recruited nine (5 males, 4 females) healthy subjects (body
mass=80.3±14.7 kg; height=179±3 cm; leg length=92±2 cm)
to participate in the study. Each subject had at least 90 min (three or more
30-min practice sessions) of previous practice walking with powered
exoskeletons and exhibited no gait abnormalities. In accordance with the
Declaration of Helsinki, subjects read and signed a consent form approved by
the University of Michigan Institutional Review Board for Human Subject
research before testing.

Exoskeletons

We custom built lightweight [mass=1.18±0.11 kg each (mean ±
s.d.)] bilateral, ankle-foot exoskeletons (i.e. orthoses) for each subject.
The exoskeletons allowed free rotation about the ankle plantar/dorsiflexion
axis. We used a metal hinge joint to connect a carbon fiber shank to a
polypropylene foot section. We used two stainless steel brackets to attach a
single artificial pneumatic muscle (length=45.6±2.2 cm; moment
arm=10.6±0.9 cm) along the posterior shank of each exoskeleton. We used
a physiologically inspired controller to command the exoskeleton plantar
flexor torque assistance with timing and amplitude derived from the user's own
soleus electromyography (i.e. proportional myoelectric control)
(Gordon and Ferris, 2007;
Sawicki and Ferris, 2008).
Specific details on the design and performance of the exoskeletons are
documented elsewhere (Ferris et al.,
2005; Ferris et al.,
2006; Gordon et al.,
2006; Sawicki and Ferris,
2008; Sawicki et al.,
2005).

Protocol

Experienced (>90 min walking with powered exoskeletons) subjects walked
on a motorized treadmill with bilateral ankle exoskeletons unpowered then
powered at four different speeds/step lengths [0.8×, 1.0×,
1.2× and 1.4× preferred step length (L*) for unpowered
walking at 1.25 m s–1]
(Donelan et al., 2002a;
Donelan et al., 2002b)
(Fig. 1; supplementary material
Movie 1). Our previous research demonstrated no further reductions in net
metabolic power (W kg–1) after 90 min of powered walking
practice (Sawicki and Ferris,
2008). We determined subjects' preferred step period (seconds)
using a stopwatch to record the mean time of three 100-step intervals during
unpowered treadmill walking at 1.25 m s–1. We took the
reciprocal of the mean step period to get the preferred step frequency (steps
s–1) at 1.25 m s–1. Then we divided the
treadmill belt speed (m s–1) by the step frequency (steps
s–1) to get the preferred step length (m
step–1) at 1.25 m s–1 (1.0 L*).
We used a metronome to enforce subjects' preferred step frequency at 1.25 m
s–1 for all conditions. We adjusted the treadmill belt speed
to constrain subjects' step lengths. The 0.8 L*, 1.0 L*,
1.2 L* and 1.4 L*, step-length conditions corresponded
to ∼1.00, 1.25, 1.50 and 1.75 m s–1 treadmill belt
speeds, respectively. We could have studied the step-to-step transition
allowing subjects to increase walking speed naturally by choosing their
preferred step length and step frequency. Instead, we chose to constrain step
frequency and vary step length, for two reasons. First, this protocol allowed
us to enforce step-to-step transition center of mass mechanical and net
metabolic power to follow a known strong proportional relationship with the
step length (∼step length4)
(Donelan et al., 2002a;
Donelan et al., 2002b) in all
walking conditions. This helped limit potential confounding effects of
frequency-dependent changes in metabolic cost between powered and unpowered
walking conditions (e.g. swing leg costs). Some estimates of swing leg
metabolic cost are as high as 33% of the total metabolic cost
(Doke et al., 2005). Second,
manipulating step length at a fixed step frequency in order to alter speed
increased the range of mechanical and net metabolic power requirements
considerably beyond what could be studied if subjects chose their preferred
step frequency at each speed. We estimate the percentage difference in step
lengths we studied compared to preferred step lengths are –12%, 0%,
+14%, and +19% for 1.0, 1.25, 1.5 and 1.75 m s–1,
respectively.

Step-length conditions were presented in random order, but for each step
length we followed the same walking timeframe
(Fig. 1). First subjects walked
for 7 min with exoskeletons unpowered (unpowered). Then subjects rested for 3
min. Finally, subjects walked for 7 min with exoskeletons powered (powered).
If the peak force output of the artificial muscles (and exoskeleton torque) is
similar in each step-length condition, then observed differences in average
exoskeleton mechanical power output across conditions would be attributed to
changes in ankle joint kinematics (range of motion, ankle joint angular
velocity) rather than changes in artificial muscle force output. Thus, we
tuned the proportional myoelectric controller during the unpowered walking
bout for each step length separately. We set the gain and threshold on soleus
surface electromyography so the control signal saturated for at least five
consecutive steps. We then doubled the gain in order to encourage reduction in
soleus muscle recruitment (Gordon and
Ferris, 2007).

Experimental set-up. Subjects walked on a motorized treadmill for 7 min
with exoskeletons unpowered, then rested for 3 min, then walked for 7 min with
exoskeletons powered, while a metronome enforced their preferred step
frequency (from unpowered walking at 1.25 m s–1). Treadmill
belt speed was set to achieve speed/step-length conditions of 0.8, 1.0, 1.2
and 1.4× the preferred step length at 1.25 m s–1
(L*; i.e. 1.00, 1.25, 1.50 and 1.75 m s–1).
Conditions were presented in randomized order. The boxes indicate periods when
data were collected (minutes 4–6) in both unpowered and powered
conditions. We collected joint kinematics using motion capture and reflective
markers, O2 consumption and CO2 production using a
metabolic cart, ankle muscle activation patterns using surface
electromyography and artificial muscle forces using series load
transducers.

Data collection and analysis

We recorded subjects' ankle, knee and hip joint kinematics, whole-body gait
kinematics, ankle dorsiflexor and plantar flexor electromyography, and
exoskeleton artificial muscle forces. For kinematic, electromyographic and
artificial muscle force data we acquired 10 s trials (i.e. ∼7–9
walking strides) at the beginning of minutes 4, 5 and 6 during each of the
eight (unpowered mode and powered mode for each of four speeds/step lengths) 7
min trials. We measured O2 consumption and CO2
production during a single 7 min quiet standing trial of metabolic data for
each subject before walking trials commenced. Metabolic data were collected
continuously during each of the 7 min speed/step-length conditions.

In addition, on a separate day of testing, we recorded metabolic data while
subjects completed each of the speed/step-length conditions on the treadmill
without (without) wearing powered exoskeletons. In the same session, we also
recorded simultaneous joint kinematics and ground reaction force data for
overground walking with unpowered exoskeletons (seven trials for each
speed/step-length condition).

Specific details on procedures for analysis of the metabolic cost,
kinematics, joint mechanics, exoskeleton mechanics and electromyography data
are identical to those in our previous research
(Sawicki and Ferris,
2008).

By combining measures of mechanical and metabolic power (W
kg–1), we computed the exoskeleton performance index and
ankle joint muscle–tendon `apparent efficiency'
(η+ankle). First, we subtracted the net metabolic
power during unpowered walking from the net metabolic power during powered
walking for each speed/step length to obtain the metabolic power savings
resulting from the exoskeleton assistance. Muscles perform positive mechanical
work with a `muscular efficiency' (η+muscle) of, on
average, ∼0.25 (ranging from 0.10–0.34)
(Gaesser and Brooks, 1975;
Margaria, 1968;
Ryschon et al., 1997;
Smith et al., 2005;
Whipp and Wasserman, 1969) and
we assumed that changes in net metabolic power would reflect the cost of the
underlying plantar flexor muscle positive mechanical work replaced by the
powered exoskeletons. Therefore, we multiplied changes in net metabolic power
by η+muscle=0.25 to yield the expected amount of
average positive mechanical power (W kg–1) delivered by the
exoskeletons for a given change in net metabolic power. Then we divided the
measured by the expected average positive mechanical power delivered by the
exoskeletons to yield the exoskeleton performance index (i.e. ankle muscle
work fraction; Eqn 1):
(1)

We inverted and scaled the performance index byη
+muscle to obtain the `apparent efficiency'
(Asmussen and Bonde-Petersen,
1974) (Eqn 2). For
example, with η+muscle=0.25, performance index=1.0
yields `apparent efficiency'=0.25 and would indicate that each joule of
exoskeleton positive mechanical work results in a 4 joule reduction in net
metabolic cost. In this case, all of the underlying ankle muscle–tendon
positive work is performed by active plantar flexor fiber shortening (muscle
work fraction=1.0) and none by previously stored elastic energy returned by
the Achilles' tendon:
(2)
It should be noted that our definition of ankle joint muscle–tendon
`apparent efficiency' allows for values >1.0. This would occur if the
performance index is <η+muscle (i.e. muscle work
fraction <η+muscle). In fact, if all of the ankle
muscle–tendon positive work was performed by Achilles' tendon recoil
with small metabolic cost, the performance index would approach zero and the
`apparent efficiency' would approach infinity. More details on this approach
can be found in our previous publication
(Sawicki and Ferris,
2008).

Joint kinematics. The thick lines show the mean ankle (left column), knee
(middle column) and hip (right column) joint angles (degrees) over the stride
from heel strike (0%) to heel strike (100%) of nine subjects. Data are
averages of left and right legs. Each row is walking data for a single
speed/step length (0.8 L* at top to 1.4 L* at bottom).
In each subplot, curves are for unpowered (black circles), and powered walking
(gray circles) and thin lines are +1 s.d. Stance is ∼0–60% of the
stride, swing 60–100%. Ankle joint plantarflexion, knee joint extension
and hip joint extension are all positive. For all joints, 0 deg. is upright
standing posture.

Statistical analyses

We used JMP IN statistical software (SAS Institute, Cary, NC, USA) to
perform a number of analysis of variance tests (ANOVAs). We set the
significance level at P<0.05 for all tests. For tests that yielded
significance we used post-hoc Tukey's honestly significant difference
(THSD) tests to determine specific differences between means. For brevity,
THSD results are only listed in text when not all pair-wise comparisons were
significant. We also computed the statistical power of each comparison.

RESULTS

Joint kinematics

During unpowered walking, as speed/step length increased, subjects walked
with increased ankle dorsiflexion, knee flexion and hip flexion early in
stance phase. Push-off phase kinematics were similar across step lengths for
the knee, but the ankle and hip joints were more extended for unpowered
walking at longer step lengths (Fig.
2).

The knee and hip joint angles over the stride were nearly identical during
powered versus unpowered walking for all speed/step-length
conditions. Ankle joint kinematics, however, were slightly altered by
exoskeleton mechanical assistance during powered walking for all
speed/step-length conditions (Fig.
2).

Ankle exoskeleton mechanics. Thick lines show the mean ankle joint angular
velocity (left column), exoskeleton torque (middle column) and exoskeleton
mechanical power (right column) over the stride from heel strike (0%) to heel
strike (100%) of nine subjects. Data are average of left and right legs. Each
row is walking data at a single speed/step length (0.8 L* at top to
1.4 L* at bottom). In each subplot, lines are for unpowered (black
circles), and powered walking (dark gray circles). Thin lines are +1 s.d.
Stance is ∼0–60% of the stride, swing 60–100%. Ankle joint
angular velocity (deg. s–1) is positive for ankle
plantarflexion. Exoskeleton torque that acts to plantar flex the ankle is
positive. Torque is the product of artificial muscle force and moment arm
length and is normalized by subject mass (Nm kg–1).
Exoskeleton mechanical power is the product of exoskeleton torque and ankle
joint angular velocity and is normalized by subject mass (W
kg–1). Positive exoskeleton mechanical power indicates
transfer of energy from exoskeletons to the user's ankle muscle–tendon
system. In the second and third columns, the ankle joint net muscle moment and
the ankle joint mechanical power from unpowered walking overground (light gray
circles) are overlaid.

Ankle joint angle was similar at heel strike but more plantar flexed
throughout early stance during powered versus unpowered walking for
all speeds/step lengths. In addition, at push-off, the ankle joint angle peak
was larger and occurred earlier during stance in powered versus
unpowered walking. For example, during unpowered 1.4 L* the ankle
joint angle peaked at 62% of the stride cycle and reached ∼+16°.
During powered 1.4 L* the ankle joint angle peaked slightly earlier
in the stride cycle and reached ∼+18°
(Fig. 2). For all speeds/step
lengths, swing phase ankle joint angle was similar during powered and
unpowered walking.

Exoskeleton mechanics

The exoskeletons produced only small amounts of torque about the ankle
during unpowered walking and delivered near zero mechanical power to the user
over the stride (Fig. 3).

As a result of increases in ankle joint angular velocity, the peak
exoskeleton mechanical power at push-off increased with speed/step length from∼
0.8 W kg–1 during powered 0.8 L* to ∼1.2
W kg–1 during powered 1.4 L*
(Fig. 3). The exoskeleton peak
mechanical power was 49% of the overground peak ankle joint mechanical power
for walking at the shortest step lengths (0.8 L*) and decreased to
31% of the overground peak ankle joint mechanical power for walking at the
longest step lengths (1.4 L*;
Fig. 3).

Average mechanical power. Bars are the mean (N=9) average
muscle–tendon (MT) positive mechanical power delivered by the sum of the
ankle, knee and hip (black bars) and the ankle muscle–tendon system only
(white bars) during unpowered overground walking. Gray bars are average
exoskeleton positive mechanical power during powered walking on the treadmill.
Error bars are ±1 s.e.m. All mechanical power values are normalized by
subject mass (W kg–1). Speeds/step lengths increase from left
0.8 L* (1.00 m s–1) to right 1.4 L*
(1.75 m s–1). Brackets indicate the percentage contribution
of bars from right to left. For example, in the 0.8 L* condition,
the exoskeleton average positive mechanical power was 70% of the ankle
muscle–tendon average positive mechanical power, ankle
muscle–tendon positive mechanical power was 34% of the ankle + knee +
hip positive mechanical power and the exoskeleton average positive mechanical
power was 24% of the ankle + knee + hip positive average positive mechanical
power over the stride.

Joint mechanics

As speed/step length increased during overground walking with unpowered
exoskeletons, the ankle, knee and hip joint muscle–tendons combined to
produce more average positive mechanical power over the stride
(Fig. 4). Average ankle
negative mechanical power was similar across speeds/step lengths, but the knee
and hip produced more average negative mechanical power over the stride as
speed/step length increased (not shown).

During overground walking with unpowered exoskeletons, the hip and ankle
produced most of the positive mechanical power at all speeds/step lengths. The
hip average positive mechanical power over the stride was 0.39±0.04 W
kg–1 at unpowered 0.8 L*, 0.47±0.05 W
kg–1 at unpowered 1.0 L*, 0.51±0.04 W
kg–1 at unpowered 1.2 L*, and 0.60±0.04 W
kg–1 at unpowered 1.4 L*. The ankle average
positive mechanical power over the stride was 0.28±0.03 W
kg–1 at unpowered 0.8 L*, 0.38±0.03 W
kg–1 at unpowered 1.0 L*, 0.52±0.03 W
kg–1 at unpowered 1.2 L*, and 0.63±0.04 W
kg–1 at unpowered 1.4 L*.

The ankle muscle–tendon system contributed a larger percentage of the
summed lower-limb muscle–tendon (ankle + knee + hip) average positive
mechanical power over the stride as speed/step length increased (34% at 0.8
L* and 39% at 1.4 L*;
Fig. 4). However, the
exoskeletons contributed a smaller percentage of the ankle muscle–tendon
positive mechanical power with increasing step length [70% at the shortest
steps (0.8 L*) and only 40% at the longest steps (1.4
L*)] (Fig. 4). As a
result, the exoskeletons delivered less of the average lower-limb positive
mechanical power over the stride during powered 1.4 L* (16%) when
compared to powered 0.8 L* (24%;
Fig. 4).

Probably as a result of added exoskeleton mass, the net metabolic power was
significantly higher (by ∼8–15%) during walking with unpowered
exoskeletons compared with walking without exoskeletons for all speeds/step
lengths except the longest 1.4 L*
(Table 1). The net metabolic
power during powered exoskeleton walking (6.19±0.29 W
kg–1) was significantly lower than for walking without
wearing exoskeletons (7.18±0.50 W kg–1) for the
longest step-length condition (Table
1).

The absolute reduction in net metabolic power in powered versus
unpowered walking increased with increasing speed/step length
(P=0.002, THSD; 1.4 L*<0.8 L*, 1.2
L*<0.8 L*; Fig.
5A). At the shortest step lengths (0.8 L*), net
metabolic power was 0.21±0.06 W kg–1 less during
powered versus unpowered walking. At 1.4 L* the reduction
in net metabolic power resulting from mechanical assistance was
0.70±0.12 W kg–1 (∼233% more than for shortest
steps). Although reductions in net metabolic power during powered walking were
larger for walking with faster speeds/longer steps, relative changes in net
metabolic power were similar between speeds/step lengths (8–12%
reduction comparing powered to unpowered;
Fig. 5A).

Gait kinematics

As expected, step length increased significantly from condition to
condition (P<0.0001) and step period was the same for all
step-length conditions (P=0.13;
Table 2). In addition, subjects
took wider steps (P<0.002) and spent less time in double support
(P<0.0001) as speed/step length increased (P<0.002;
Table 2).

There were no significant differences in step period (P>0.47),
step width (P>0.37), or double support time (P>0.27),
between powered and unpowered walking at any step length. Step length was
shorter by ∼1% during powered walking at 1.0 L*
(P=0.04; Table 2).

DISCUSSION

Our results suggest that as speed/step length increased from 80% to 140% of
the preferred step length (1.00–1.75 m s–1) the
metabolic cost of ankle muscle–tendon positive mechanical work increased
from 7% to 26% of the total metabolic cost of walking. The increased metabolic
cost of ankle muscle–tendon positive work is due to a small increase in
the relative contribution of the plantar flexor muscle–tendons to the
total lower-limb muscle–tendon positive mechanical work (from 34% to
40%), and a large decrease in the `apparent efficiency' of the ankle joint
muscle–tendon system (from 1.39 to 0.38) with increasing speed/step
length.

With powered ankle exoskeletons, subjects saved more than three times the
absolute net metabolic power (W kg–1) in the longest (1.4
L*) compared with the shortest (0.8 L*) step-length
condition, but relative reductions in metabolic cost were similar across
speeds/step lengths (8–12%; Fig.
5A). This was because exoskeletons performed a progressively
smaller percentage of ankle muscle–tendon (and total lower-limb
muscle–tendon) average positive mechanical power at faster speeds with
longer step lengths (Figs 3 and
4). Normally the human ankle
muscle–tendon system generates more positive mechanical power during
push-off as walking speed increases by increasing the magnitudes of both the
ankle joint plantar flexor moment and the ankle joint plantar flexor angular
velocity (Craik and Oatis,
1995; Winter,
1984). In the present study, although the ankle joint angular
velocity increased near push-off with increasing walking speed/step length,
the peak torque generated by the exoskeletons was very similar across
speeds/step lengths. Increases in exoskeleton average mechanical power were
due almost entirely to increases in ankle joint angular velocity. Exoskeletons
delivered more average mechanical power over the stride with increasing
speed/step length, but they could not match the magnitude of the increases in
the biological ankle joint moment with speed/step length.

The validity of our estimates for both the relative metabolic cost (% of
total cost of walking) and the `apparent efficiency' of ankle
muscle–tendon positive work depends on a key assumption. We based our
calculations on the expectation that changes in subjects' net metabolic power
could be attributed to powered exoskeleton mechanical work directly replacing
a portion of the ankle muscle–tendon positive mechanical work during
push-off. There are a number of factors that could have influenced the
validity of this assumption.

Subjects could have increased their total average external mechanical power
in response to exoskeleton mechanical assistance. A higher average external
mechanical power during powered versus unpowered walking would
indicate that subjects used exoskeleton energy to augment rather than replace
biological muscle–tendon positive mechanical work. This would make it
difficult to attribute changes in subjects' net metabolic power to exoskeleton
assistance isolated at the ankle joint rather than to differences in overall
gait characteristics. Net metabolic power during walking increases with
increasing speed/step length (Donelan et
al., 2002a), step frequency
(Bertram and Ruina, 2001), and
step width (Donelan et al.,
2001). We held step frequency constant (using a metronome) and
used treadmill belt speed to vary the step length
(Table 2). Keeping step length
and step frequency constant highly constrains the average external mechanical
power to be similar for unpowered and powered walking. We also measured step
width and found no differences between unpowered and powered walking during
any step-length condition (Table
2).

Even with nearly constant external average mechanical power, subjects still
could have altered the distribution of mechanical power across the joints
between unpowered and powered walking. For example, during powered walking,
increased ankle muscle–tendon positive mechanical power could have been
offset by compensatory muscle–tendon mechanical power at the knee or
hip. In this study, subjects were limited to walking on a motorized treadmill
during powered conditions because of the tethered pneumatic hoses connecting
exoskeleton artificial pneumatic muscles to a pressurized air source. Since
our treadmill was not instrumented with force platforms, we could not compare
joint powers using inverse dynamics for unpowered and powered walking to rule
out redistribution of mechanical power. However, recent results from our lab
indicate no difference in total ankle joint moment patterns when comparing
powered and unpowered exoskeleton walking
(Lewis et al., 2008).

Our joint kinematic and electromyography data provide good evidence that
subjects did not redistribute joint mechanical power as a result of mechanical
assistance from the exoskeletons. During powered walking, the ankle joint was
slightly more plantar flexed during stance, but the knee and hip joint
kinematics were nearly identical for powered and unpowered walking
(Fig. 2). Furthermore, in the
current study during powered walking, the exoskeletons delivered 32% of the
peak ankle muscle–tendon moment and 48% of the peak ankle
muscle–tendon mechanical power observed during overground unpowered
walking trials. In response, subjects significantly decreased muscle activity
in their ankle plantar flexors. Reductions in plantar flexor r.m.s. EMG
provides additional support for the idea that the total ankle joint moment
(and presumably mechanical power) was maintained between unpowered and powered
conditions.

Reductions in soleus r.m.s. EMG (maximum of 20%) were larger than in medial
gastrocnemius (maximum of 13%) and lateral gastrocnemius (maximum of 15%;
Fig. 6). The larger reductions
in soleus are consistent with our previous research using powered exoskeletons
(20–30% reductions) (Cain et al.,
2007; Gordon and Ferris,
2007; Sawicki and Ferris,
2008). It is possible that reductions in the biarticular
gastrocnemius muscles due to powered assistance were smaller than in soleus
because of their functional role in assisting with swing leg initiation
(Meinders et al., 1998;
Neptune et al., 2001) or in
transferring mechanical energy from proximal muscle–tendons
(Zajac et al., 2002). Another
possibility is that the neural mechanism behind soleus muscle activation is
fundamentally different than for medial gastrocnemius and lateral
gastrocnemius (e.g. feedback versus feedforward dominated). Recent
evidence indicates that positive force feedback via type Ib afferents
contributes significantly to soleus muscle activity
(Grey et al., 2007) and
suggests that reductions in soleus muscle activity during powered
versus unpowered walking may reflect reduced positive force feedback
due to partial unloading of the Achilles' tendon.

Subjects could also have responded to added ankle joint mechanical power by
increasing dorsiflexor activation. Muscle co-activation is an indicator of
simultaneous positive and negative muscle–tendon work and can
significantly increase the metabolic cost of walking
(Winter, 1990). To address
this possibility, we recorded tibialis anterior (the major ankle dorsiflexor)
surface electromyography, for both unpowered and powered walking at each
speed/step length (Fig. 6).
Tibialis anterior r.m.s. EMG was not elevated during powered walking at any of
the speeds/step lengths we tested. Although we did not measure EMG to check
for co-activation at more proximal joints, our previous research has indicated
no differences in the vastii, rectus femoris, and medial hamstrings between
powered and unpowered ankle exoskeleton walking
(Gordon and Ferris, 2007).

Finally, we also assumed that mechanical work performed by the net ankle
muscle–tendon moment is an accurate estimate of the underlying
mechanical work performed by the ankle plantar flexor muscles and Achilles'
tendon recoil during the push-off phase of walking. The biarticular
gastrocnemius muscles can theoretically transfer mechanical energy to and from
the ankle joint via the knee and/or hip
(Neptune et al., 2004a;
Zajac et al., 2002). However,
according to a computer simulation analysis, during the stance phase of
walking the energy transfers between the knee and ankle do not significantly
confound the accuracy of muscle work estimates based on net moment work
(Prilutsky et al., 1996). In
addition, co-activation of antagonist muscles could have confounded estimates
of plantar flexor muscle work that are based on net ankle joint mechanical
power. This possibility is unlikely at the ankle joint during the step-to-step
transition of walking. During this phase, medial gastrocnemius and lateral
gastrocnemius each perform positive work at both the ankle and knee while
soleus performs positive work only at the ankle. But because there is no
simultaneous negative work by ankle dorsiflexors (i.e. tibialis anterior)
occurring, the positive mechanical work delivered at the ankle joint by the
triceps surae (soleus, medial and lateral gastrocnemius) is all accounted for
by integrating the net ankle joint mechanical power.

Given the validity of our aforementioned assumptions, our results indicate
that the ankle muscle–tendon system performs positive mechanical work
during walking with remarkably high `apparent efficiency', even when
increasing speed with longer step lengths. Studies indicate that actively
shortening mammalian muscle fibers perform mechanical work with a `muscular
efficiency', on average, ∼0.25 (0.10–0.34)
(Gaesser and Brooks, 1975;
Margaria, 1968;
Ryschon et al., 1997;
Smith et al., 2005;
Whipp and Wasserman, 1969). In
the current study, as walking speed/step length increased, the ankle
muscle–tendon system performed positive mechanical work with lower
`apparent efficiency' (Fig.
5C). But even in the longest step-length condition (1.4
L*), the ankle was more efficient (∼0.38) than muscle in
isolation. These results suggest that the Achilles' tendon contributes a
significant portion of the positive work performed by the ankle
muscle–tendon system during walking, at all speeds/step lengths we
studied.

Assuming muscle positive work is performed withη
+muscle=0.25 and accounts for the whole metabolic
cost of ankle muscle–tendon work, we can compute an estimate of the
upper limit on the fraction of ankle muscle–tendon positive work
performed by muscles (i.e. exoskeleton performance index=ankle muscle work
fraction=η+muscle/η+ankle)
(Sawicki and Ferris, 2008).
For walking at 0.8 L* (∼1.00 m s–1), we
estimate that plantar flexor muscles perform at most 18% (i.e.
0.25/1.39×100) of the total ankle muscle–tendon positive work. The
Achilles' tendon, therefore, must perform the remaining 82% of the ankle
muscle–tendon positive work by returning previously stored elastic
energy during push-off. Similarly, for walking at 1.4 L* (∼1.75
m s–1), we estimate that plantar flexors perform at most 66%
and the Achilles' tendon at least 34% of the total ankle muscle–tendon
positive work.

Our suggestion that Achilles' tendon elastic energy storage and return is
significant during walking is consistent with recent in vivo
ultrasound data from humans (Fukunaga et
al., 2001; Ishikawa et al.,
2005; Ishikawa et al.,
2006; Lichtwark and Wilson,
2006). Ishikawa et al. showed that during walking at 1.4 m
s–1, the soleus and medial gastrocnemius act nearly
isometrically to support a `catapult action' in the Achilles' tendon
(Ishikawa et al., 2005).
Negative work is stored in the triceps surae–Achilles' tendon unit over
the first 70% and then released rapidly over the final 30% of the stance phase
(i.e. in the push-off phase of the step-to-step transition). Rough integration
of the reported mechanical power curves for the muscle–tendon unit, and
the tendon only, suggests that the vast majority (>80%) of the positive
work performed by the muscle–tendon during push-off is delivered by the
recoiling Achilles' tendon (Ishikawa et
al., 2005). Our data from similar walking speeds (1.0
L* and 1.2 L* are ∼1.25 and ∼1.5 m
s–1) suggest that the Achilles' tendon performs at least
44–59% of the total ankle muscle–tendon work.

Our results suggest that the relative metabolic cost of ankle
muscle–tendon mechanical work increases with speed/step length during
walking. The ankle muscle–tendon system provides a significant fraction
of the total positive lower-limb muscle–tendon mechanical work that
increases slightly with speed/step length (from 34% to 40%;
Fig. 4). In addition, ankle
plantar flexor muscles perform a larger fraction of the total ankle
muscle–tendon positive work at faster speeds/longer step lengths,
driving down the `apparent efficiency' of ankle muscle–tendon positive
work (from 1.39 to 0.38; Fig.
5C). In short, as speed/step length increases, the ankle
muscle–tendon system performs a larger fraction of the total lower-limb
muscle–tendon mechanical work with lower `apparent efficiency'.
Therefore, the fraction of the total net metabolic cost (W
kg–1) of walking due to ankle muscle–tendon positive
mechanical work increases at faster speeds/longer step lengths.

As step length increases from 80% to 140% of preferred, we estimate that
the ankle muscle–tendon system consumes ∼18% more of the total net
metabolic power (W kg–1) during walking. For example, at 0.8
L* the percentage of the summed lower-limb muscle–tendon
(ankle + knee + hip) average positive mechanical power that is delivered by
the ankle muscle–tendon system is 34%. The `apparent efficiency'
lower-limb muscle–tendon positive mechanical work at 0.8 L*
is 0.29 [i.e. lower-limb muscle–tendon average positive mechanical power
(0.83 W kg–1)/net metabolic power (2.86 W
kg–1)=0.29]. The `apparent efficiency' of only the ankle
muscle–tendon positive mechanical work is 1.39. Thus, the percentage of
the total net metabolic power (W kg–1) due to ankle
muscle–tendon positive work is 34%×0.29/1.39=7%. Similar
calculations can be carried out for the other speed/step-length conditions.
The percentage of muscle–tendon average positive mechanical power from
the ankle is 36%, 40% and 39% for the 1.0 L*–1.4
L* step-length conditions. Over the same range of step lengths, the
`apparent efficiency' of total lower-limb muscle–tendon positive
mechanical work is 0.31, 0.29 and 0.23 and the ankle muscle–tendon
`apparent efficiency' is 0.61, 0.45 and 0.38. Thus, we estimate the ankle
muscle–tendon system consumes 18%, 26% and 24% of the total net
metabolic power (W kg–1) for walking as speed/step length
increases from preferred (1.25 m s–1) to 140% preferred (1.75
m s–1).

The metabolic cost of walking may be dominated by positive muscle work at
the proximal joints (i.e. hip and knee). Our results suggest that humans can
save a significant amount of metabolic energy at the distal ankle joint by
using previously stored Achilles' tendon elastic energy to partially power
push-off during the step-to-step transition. As a result, in the worst case
(i.e. 1.2 L*), the ankle muscle–tendon system consumes 26% of
the total net metabolic energy but produces 40% of the total positive
mechanical work during walking. So where is the remaining 74% of the metabolic
energy spent? Keeping along the lines of lower-limb muscle–tendon work,
we feel that the hip joint muscle–tendon system might consume a large
portion of unaccounted metabolic energy. The hip supplies positive mechanical
work on par with the ankle (∼30–40% of the total lower-limb
muscle–tendon positive work). But the morphology (i.e. long muscle
fibers and short or no tendons) of the human hip may significantly reduce its
`apparent efficiency' to perform positive mechanical work. It is likely that
the positive work supplied by the hip muscle–tendon system is performed
almost exclusively by active muscle shortening rather than passive tendon
recoil. At the preferred step length, if the combined knee/hip positive
mechanical work (64% of the total) accounts for the remaining 82% of the
metabolic cost of walking then we estimate the combined knee/hip
muscle–tendon `apparent efficiency' is ∼0.24.

Implications and future research

From a basic science perspective, our long-term goal is to establish a
joint-based relationship between the mechanics and energetics of human
locomotion. We hope to be able to approximately explain the metabolic cost of
human walking as the sum of the metabolic cost of muscle–tendons
performing positive work at each of the lower-limb joints (ankle + knee +
hip). With measurements of average positive mechanical power and the `apparent
efficiency' of positive mechanical work for muscle–tendons spanning each
joint this should be possible. Therefore, future studies should examine the
`apparent efficiency' of the hip and knee muscle–tendons under various
walking conditions.

The importance of elastic energy storage and return in the Achilles' tendon
during walking sheds light on an alternative way to view ankle exoskeleton
mechanical assistance. Even if ankle plantar flexors perform little muscular
work during human walking, they must still act like struts, producing the
forces necessary to support body weight and series tendon elastic energy
storage and return (Griffin et al.,
2003; Pontzer,
2005). This may be a useful perspective to take when trying to
understand changes in net metabolic power that result from powering lower-limb
joints where elastic energy cycling is important (i.e. the ankle). For
example, regardless of the work that exoskeleton artificial muscles perform,
the torque that they develop about the ankle reduces the forces required from
biological ankle plantar flexors. Although we did not use net ankle joint
muscle–tendon moment data to estimate reductions in muscle forces, it
should be possible to calculate an `apparent economy' of ankle plantar flexor
force production to gain insight into the relative metabolic costs of
generating muscle force versus performing muscle work during human
walking.

Considerable effort has been placed on developing assistive devices (i.e.
exoskeletons and prostheses) designed to reduce the metabolic cost of walking
(Guizzo and Goldstein, 2005).
From an applied science perspective, our results suggest that metabolic energy
savings are likely to be much more modest than expected when using an
exoskeleton to supplant muscle–tendon work at distal, compliant joints.
Instead, powering joints where active muscle rather than recoiling tendon
performs most of the positive mechanical work (i.e. powering the less
efficient joints) may lead to larger reductions in metabolic cost
(Ferris et al., 2007).
Furthermore, passive devices designed to reduce isometric muscle forces during
periods of tendon stretch and recoil could also be useful at relatively
elastic joints (i.e. ankle).

LIST OF ABBREVIATIONS

EMG

electromyography

L*

preferred step length

r.m.s.

root mean square

Speed/step length

increasing speed by varying step length at fixed step
frequency

TA

tibialis anterior

η+ankle

ankle muscle–tendon `apparent efficiency' of positive mechanical
work

η+muscle

`muscular efficiency' of positive mechanical work

FOOTNOTES

This research was supported by NSF
BES-0347479 to D.P.F. We would like to thank Catherine
Kinnaird, Jineane Shibuya and other members of the Human Neuromechanics
Laboratory for assisting with data collection and analysis. Jacob Godak and
Anne Manier of the University of Michigan Orthotics and Prosthetics Center
built the exoskeletons.

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